Abstract: The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time $T_{\rm c}$ as a function of $\lambda$ (the correlated intensity between noises) exhibits very different behaviours for $\alpha < D$ and for $\alpha > D$ ($\alpha$ and $D$, respectively, stand for the ntensities of additive and multiplicative noises). When $\alpha < D$, $T_{\rm c}$ increases with increasing $\lambda$. But when $\alpha < D$, $T_{\rm c}$ increases with $\lambda$ for the case of weak correlated noises and sharply decreases with $\lambda$ for the case of strong correlated noises, and thus $T_{\rm c}$-$\lambda$ curve behaves with one extremum.

Key words: correlated noise, relaxation time, bistable system